Proceedings of the COLING/ACL 2006 Main Conference Poster Sessions, pages 803–810, Sydney, July 2006. c 2006 Association for Computational Linguistics Discourse Generation Using Utility-Trained Coherence Models Radu Soricut Information Sciences Institute University of Southern California 4676 Admiralty Way, Suite 1001 Marina del Rey, CA 90292 radu@isi.edu Daniel Marcu Information Sciences Institute University of Southern California 4676 Admiralty Way, Suite 1001 Marina del Rey, CA 90292 marcu@isi.edu Abstract We describe a generic framework for inte- grating various stochastic models of dis- course coherence in a manner that takes advantage of their individual strengths. An integral part of this framework are algo- rithms for searching and training these stochastic coherence models. We evaluate the performance of our models and algo- rithms and show empirically that utility- trained log-linear coherence models out- perform each of the individual coherence models considered. 1 Introduction Various theories of discourse coherence (Mann and Thompson, 1988; Grosz et al., 1995) have been applied successfully in discourse analy- sis (Marcu, 2000; Forbes et al., 2001) and dis- course generation (Scott and de Souza, 1990; Kib- ble and Power, 2004). Most of these efforts, how- ever, have limited applicability. Those that use manually written rules model only the most visi- ble discourse constraints (e.g., the discourse con- nective “although” marks a CONCESSION relation), while being oblivious to fine-grained lexical indi- cators. And the methods that utilize manually an- notated corpora (Carlson et al., 2003; Karamanis et al., 2004) and supervised learning algorithms have high costs associated with the annotation pro- cedure, and cannot be easily adapted to different domains and genres. In contrast, more recent research has focused on stochastic approaches that model discourse coher- ence at the local lexical (Lapata, 2003) and global levels (Barzilay and Lee, 2004), while preserving regularities recognized by classic discourse theo- ries (Barzilay and Lapata, 2005). These stochas- tic coherence models use simple, non-hierarchical representations of discourse, and can be trained with minimal human intervention, using large col- lections of existing human-authored documents. These models are attractive due to their increased scalability and portability. As each of these stochastic models captures different aspects of co- herence, an important question is whether we can combine them in a model capable of exploiting all coherence indicators. A frequently used testbed for coherence models is the discourse ordering problem, which occurs often in text generation, complex question answer- ing, and multi-document summarization: given discourse units, what is the most coherent order- ing of them (Marcu, 1996; Lapata, 2003; Barzilay and Lee, 2004; Barzilay and Lapata, 2005)? Be- cause the problem is NP-complete (Althaus et al., 2005), it is critical how coherence model evalua- tion isintertwined with search: if the search for the best ordering is greedy and has many errors, one is not able to properly evaluate whether a model is better than another. If the search is exhaustive, the ordering procedure may take too long to be useful. In this paper, we propose an A search al- gorithm for the discourse ordering problem that comes with strong theoretical guarantees. For a wide range of practical problems (discourse order- ing of up to 15 units), the algorithm finds an op- timal solution in reasonable time (on the order of seconds). A beam search version of the algorithm enables one to find good, approximate solutions for very large reordering tasks. These algorithms enable us not only to compare head-to-head, for the first time, a set of coherence models, but also to combine these models so as to benefit from their complementary strengths. The model com- 803 bination is accomplished using statistically well- founded utility training procedures which auto- matically optimize the contributions of the indi- vidual models on a development corpus. We em- pirically show that utility-based models of dis- course coherence outperform each of the individ- ual coherence models considered. In the following section, we describe previously-proposed and new coherence models. Then, we present our search algorithms and the input representation they use. Finally, we show evaluation results and discuss their implications. 2 Stochastic Models of Discourse Coherence 2.1 Local Models of Discourse Coherence Stochastic local models of coherence work under the assumption that well-formed discourse can be characterized in terms of specific distributions of local recurring patterns. These distributions can be defined at the lexical level or entity-based levels. Word-Coocurrence Coherence Models. We propose a new coherence model, inspired by (Knight, 2003), that models the intuition that the usage of certain words in a discourse unit (sentence) tends to trigger the usage of other words in subsequent discourse units. (A similar intuition holds for the Machine Translation mod- els generically known as the IBM models (Brown et al., 1993), which assume that certain words in a source language sentence tend to trigger the usage of certain words in a target language translation of that sentence.) We train models able to recognize local recur- ring patterns of word usage across sentences in an unsupervised manner, by running an Expectation- Maximization (EM) procedure over pairs of con- secutive sentences extracted from a large collec- tion of training documents 1 . We expect EM to detect and assign higher probabilities to recur- ring word patterns compared to casually occurring word patterns. A local coherence model based on IBM Model 1 assigns the following probability to a text con- sisting of sentences : 1 We use for training the publicly-available GIZA++ toolkit, http://www.fjoch.com/GIZA++.html We call the above equation the direct IBM Model 1, as this model considers the words in sen- tence (the events) as being generated by the words in sentence (the events, which in- clude the special event called the NULL word), with probability . We also define a local coherence inverse IBM Model 1: This model considers the words in sentence (the events) as being generated by the words in sen- tence (the events, which include the spe- cial event called the NULL word), with prob- ability . Entity-based Coherence Models. Barzilay and Lapata (2005) recently proposed an entity-based coherence model that aims to learn abstract coher- ence properties, similar to those stipulated by Cen- tering Theory (Grosz et al., 1995). Their model learns distribution patterns for transitions between discourse entities that are abstracted into their syn- tactic roles – subject (S), object (O), other (X), missing (-). The feature values are computed us- ing an entity-grid representation for the discourse that records the syntactic role of each entity as it appears in each sentence. Also, salient entities are differentiated from casually occurring entities, based on the widely used assumption that occur- rence frequency correlates with discourse promi- nence (Morris and Hirst, 1991; Grosz et al., 1995). We exclude the coreference information from this model, as the discourse ordering problem can- not accommodate current coreference solutions, which assume a pre-specified order (Ng, 2005). In the jargon of (Barzilay and Lapata, 2005), the model we implemented is called Syntax+Salience. The probability assigned to a text by this Entity-Based model (henceforth called EB) can be locally computed (i.e., at sentence transi- tion level) using feature functions, as follows: Here, are feature values, and are weights trained to discriminate between coher- ent, human-authored documents and examples as- sumed to have lost some degree of coherence (scrambled versions of the original documents). 2.2 Global Models of Discourse Coherence Barzilay and Lee (2004) propose a document con- tent model that uses a Hidden Markov Model 804 (HMM) to capture more global aspects of coher- ence. Each state in their HMM corresponds to a distinct “topic”. Topics are determined by an un- supervised algorithm via complete-link clustering, and are written as , with . The probability assigned to a text by this Content Model (henceforth called CM) can be written as follows: The first term, , models the probability of changing from topic to topic . The second term, , models the probability of generating sentences from topic . 2.3 Combining Local and Global Models of Discourse Coherence We can model the probability of a text us- ing a log-linear model that combines the discourse coherence models presented above. In this frame- work, we have a set of feature functions , . For each feature function, there ex- ists a model parameter , . The probability can be written under the log- linear model as follows: Under this model, finding the most probable text is equivalent with solving Equation 1, and there- fore we do not need to be concerned about com- puting expensive normalization factors. (1) In this framework, we distinguish between the modeling problem, which amounts to finding ap- propriate feature functions for the discourse co- herence task, and the training problem, which amounts to finding appropriate values for , . We address the modeling problem by using as feature functions the discourse coherence models presented in the previous sections. In Sec- tion 3, we address the training problem by per- forming a discriminative training procedure of the parameters, using as utility functions a metric that measures how different a training instance is from a given reference. "−Name− ( −Name− ) a strong earthquake hit the −Name− −Name− in northwestern −Name− early −Name− the official −Name− −Name− −Name− reported ## −−−−−−−−−SXXOSXOXSSS−" γ: information injuries damage magnitude quake area GMT It BC−China Altai S − − − − X − − S X − − X − − X − − O − − X − − − Wednesday Xinhua News Agency S S − −− − BC−China−Earthquake|Urgent Earthquake rocks northwestern Xinjiang Mountains AP Earthquake northwestern Xinjiang Mountains Beijing O O O X X − − − − − S X − − O S S − S − −− − XO − − S − B: C: (a) "it said no information had been received about injuries or damage from the magnitude +.+ quake which struck the sparsely inhabited area at + ++ am ( ++++ gmt ) ## SSXXXXOX−−−−−−−−−−−−−" α: A: It said no information had been received about injuries or damage from the mag− nitude 6.1 quake which struck the sparsely inhabited area at 2 43 AM (1843 GMT) Xinjiang early Wednesday the official Xinhua News Agency reported Beijing (AP) A strong earthquake hit the Altai Mountains in northwestern "−−−−−−−−" "−Name− earthquake rocks northwestern −Name− −Name− ## −−−−−−−−SSOOO β: (b) (c) Figure 1: Example consisting of discourse units A, B, and C (a). In (b), their entities are detected (underlined) and assigned syntactic roles: S (sub- ject), O (object), X (other), - (missing). In (c), terms , and encode these discourse units for model scoring purposes. 3 Search Algorithms for Coherent Discourses and Utility-Based Training The algorithms we propose use as input repre- sentation the IDL-expressions formalism (Neder- hof and Satta, 2004; Soricut and Marcu, 2005). We use here the IDL formalism (which stands for Interleave, Disjunction, Lock, after the names of its operators) to define finite sets of possible dis- courses over given discourse units. Without losing generality, we will consider sentences as discourse units in our examples and experiments. 3.1 Input Representation Consider the discourse units A-C presented in Fig- ure 1(a). Each of these units undergoes various processing stages in order to provide the infor- mation needed by our coherence models. The entity-based model (EB) (Section 2), for instance, makes use of a syntactic parser to determine the syntactic role played by each detected entity (Fig- ure 1(b)). For example, the string SSXXXXOX- - (first row of the grid in Figure 1(b), corresponding to discourse unit A) encodes that and have subject (S) role, , etc. have other (X) roles, has object (O) role, and the rest of the entities do not appear (-) in this unit. In order to be able to solve Equation 1, the input representation needs to provide the neces- sary information to compute all terms, that is, all individual model scores. Textual units A, B, 805 d ε ε /dβ γ α v v 3 5 4 v v 6 2 vv 1 v s v e Figure 2: The IDL-graph corresponding to the IDL-expression . and C in our example are therefore represented as terms , and , respectively 2 (Figure 1(c)). These terms act like building blocks for IDL- expressions, as in the following example: uses the (Interleave) operator to create a bag- of-units representation. That is, E stands for the set of all possible order permutations of , and , with the additional information that any of these orders are to appear between the beginning and end of document . An equivalent represen- tation, called IDL-graphs, captures the same in- formation using vertices and edges, which stand in a direct correspondence with the operators and atomic symbols of IDL-expressions. For instance, each and –labeled edge -pair, and their source and target vertices, respectively, correspond to a -argument operator. In Figure 2, we show the IDL-graph corresponding to IDL-expression . 3.2 Search Algorithms Algorithms that operate on IDL-graphs have been recently proposed by Soricut and Marcu (2005). We extend these algorithms to take as input IDL- graphs over non-atomic symbols (such that the co- herence models can operate inside terms like , and from Figure 1), and also to work under models with hidden variables such as CM (Sec- tion 2.2). These algorithm, called IDL-CH-A (A search for IDL-expressions under Coherence models) and IDL-CH-HB (Histogram-Based beam search for IDL-expressions under Coherence models, with histogram beam ), assume an alphabet of non- atomic (visible) variables (over which the input IDL-expressions are defined), and an alphabet of hidden variables. They unfold an input IDL- graph on-the-fly, as follows: starting from the initial vertex , the input graph is traversed in an IDL-specific manner, by creating states which 2 Following Barzilay and Lee (2004), proper names, dates, and numbers are replaced with generic tokens. keep track of positions in any subgraph cor- responding to a -argument operator, as well as the last edge traversed and the last hidden variable considered. For instance, state (see the blackened vertices in Fig- ure 2) records that expressions and have al- ready been considered (while is still in the fu- ture of state ), and was the last one considered, evaluated under the hidden variable . The infor- mation recorded in each state allows for the com- putation of a current coherence cost under any of the models described in Section 2. In what fol- lows, we assume this model to be the model from Equation 1, since each of the individual models can be obtained by setting the other s to 0. We also define an admissible heuristic func- tion (Russell and Norvig, 1995), which is used to compute an admissible future cost for state , using the following equation: is the set of future (visible) events for state , which can be computed directly from an input IDL-graph, as the set of all –edge-labels between the vertices of state and final vertex . For example, for state , we have . is the set of future (visible) conditions for state , which can be obtained from (any non-final future event may become a fu- ture conditioning event), by eliminating and adding the current conditioning event of . For the considered example state , we have . The value is admissible because, for each fu- ture event , with and , its cost is computed using the most inexpensive condition- ing event . The IDL-CH-A algorithm uses a priority queue (sorted according to total cost, computed as current admissible) to control the unfolding of an input IDL-graph, by processing, at each un- folding step, the most inexpensive state (extracted from the top of ). The admissibility of the fu- ture costs and the monotonicity property enforced by the priority queue guarantees that IDL-CH-A finds an optimal solution to Equation 1 (Russell and Norvig, 1995). The IDL-CH-HB algorithm uses a histogram beam to control the unfolding of an input IDL- graph, by processing, at each unfolding step, the 806 top most inexpensive states (according to to- tal cost). This algorithm can be tuned (via ) to achieve good trade-off between speed and accu- racy. We refer the reader to (Soricut, 2006) for additional details regarding the optimality and the theoretical run-time behavior of these algorithms. 3.3 Utility-based Training In addition to the modeling problem, we must also address the training problem, which amounts to finding appropriate values for the parameters from Equation 1. The solution we employ here is the discrimina- tive training procedure of Och (2003). This proce- dure learns an optimal setting of the parame- ters using as optimality criterion the utility of the proposed solution. There are two necessary ingre- dients to implement Och’s (2003) training proce- dure. First, it needs a search algorithm that is able to produce ranked -best lists of the most promis- ing candidates in a reasonably fast manner (Huang and Chiang, 2005). We accommodate -best computation within the IDL-CH-HB algorithm, which decodes bag-of-units IDL-expressions at an average speed of 75.4 sec./exp. on a 3.0 GHz CPU Linux machine, for an average input of 11.5 units per expression. Second, it needs a criterion which can automati- cally assess the quality of the proposed candidates. To this end, we employ two different metrics, such that we can measure the impact of using different utility functions on performance. TAU (Kendall’s ). One of the most frequently used metrics for the automatic evaluation of doc- ument coherence is Kendall’s (Lapata, 2003; Barzilay and Lee, 2004). TAU measures the mini- mum number of adjacent transpositions needed to transform a proposed order into a reference order. The range of the TAU metric is between -1 (the worst) to 1 (the best). BLEU. One of the most successful metrics for judging machine-generated text is BLEU (Pap- ineni et al., 2002). It counts the number of un- igram, bigram, trigram, and four-gram matches between hypothesis and reference, and combines them using geometric mean. For the discourse or- dering problem, we represent hypotheses and ref- erences by index sequences (e.g., “4 2 3 1” is a hy- pothesis order over four discourse units, in which the first and last units have been swapped with re- spect to the reference order). The range of BLEU scores is between 0 (the worst) and 1 (the best). We run different discriminative training ses- sions using TAU and BLEU, and train two differ- ent sets of the parameters for Equation 1. The log-linear models thus obtained are called Log- linear and Log-linear , respectively. 4 Experiments We evaluate empirically two different aspects of our work. First, we measure the performance of our search algorithms across different models. Second, wecompare the performance of each indi- vidual coherence model, and also the performance of the discriminatively trained log-linear models. We also compare the overall performance (model & decoding strategy) obtained in our framework with previously reported results. 4.1 Evaluation setting The task on which we conduct our evaluation is information ordering (Lapata, 2003; Barzilay and Lee, 2004; Barzilay and Lapata, 2005). In this task, a pre-selected set of information-bearing document units (in our case, sentences) needs to be arranged in a sequence which maximizes some specific information quality (in our case, docu- ment coherence). We use the information-ordering task as a means to measure the performance of our algorithms and models in a well-controlled setting. As described in Section 3, our framework can be used in applications such as multi-document sum- marization. In fact, Barzilay et al. (2002) formu- late the multi-document summarization problem as an information ordering problem, and show that naive ordering algorithms such as majority order- ing (select most frequent orders across input docu- ments) and chronological ordering (order facts ac- cording to publication date) do not always yield coherent summaries. Data. For training and testing, we use docu- ments from two different genres: newspaper arti- cles and accident reports written by government officials (Barzilay and Lapata, 2005). The first collection (henceforth called EARTHQUAKES) consists of Associated Press articles from the North American News Corpus on the topic of nat- ural disasters. The second collection (henceforth called ACCIDENTS) consists of aviation accident reports from the National Transportation Safety 807 Search Algorithm IBM IBM CM EB ESE TAU BLEU ESE TAU BLEU ESE TAU BLEU ESE TAU BLEU EARTHQUAKES IDL-CH-A 0% .39 .12 0% .33 .13 0% .39 .12 0% .19 .05 IDL-CH-HB 0% .38 .12 0% .32 .13 0% .39 .12 0% .19 .06 IDL-CH-HB 4% .37 .13 13% .34 .14 36% .32 .11 16% .18 .05 Lapata, 2003 90% .01 .04 58% .02 .06 97% .05 .04 46% 05 .00 ACCIDENTS IDL-CH-A 0% .41 .21 0% .40 .21 0% .37 .15 0% .13 .10 IDL-CH-HB 0% .41 .20 0% .40 .21 2% .36 .15 0% .12 .10 IDL-CH-HB 0% .38 .19 12% .32 .20 13% .34 .13 33% 04 .06 Lapata, 2003 86% .11 .03 67% .12 .05 85% .18 .00 24% 05 .06 Table 1: Evaluation of search algorithms for document coherence, for both EARTHQUAKES and ACCIDENTS genres, across the IBM , IBM , CM, and EB models. Performance is measured in terms of percentage of Estimated Search Errors (ESE), as well as quality of found realizations (average TAU and BLEU). Model TAU BLEU TAU BLEU EARTHQUAKES ACCIDENTS IBM .38 .12 .41 .20 IBM .32 .13 .40 .21 CM .39 .12 .36 .15 EB .19 .06 .12 .10 Log-linear .34 .14 .48 .23 Log-linear .47 .15 .50 .23 Log-linear .46 .16 .49 .24 Table 2: Evaluation of stochastic models for doc- ument coherence, for both EARTHQUAKES and ACCIDENTS genre, using IDL-CH-HB . Board’s database. For both collections, we used 100 documents for training and 100 documents for testing. A frac- tion of 40% of the training documents was tem- porarily removed and used as a development set, on which we performed the discriminative train- ing procedure. 4.2 Evaluation of Search Algorithms We evaluated the performance of several search algorithms across four stochastic models of doc- ument coherence: the IBM and IBM coher- ence models, the content model of Barzilay and Lee (2004) (CM), and the entity-based model of Barzilay and Lapata (2005) (EB) (Section 2). We measure search performance using an Estimated Search Error (ESE) figure, which reports the per- centage of times when the search algorithm pro- poses a sentence order which scores lower than Overall performance TAU QUAKES ACCID. Lapata (2003) 0.48 0.07 Barzilay & Lee (2004) 0.81 0.44 Barzilay & Lee (reproduced) 0.39 0.36 Barzilay & Lapata (2005) 0.19 0.12 IBM , IDL-CH-HB 0.38 0.41 Log-lin , IDL-CH-HB 0.47 0.50 Table 3: Comparison of overall performance (af- fected by both model & search procedure) of our framework with previous results. the original sentence order (OSO). We also mea- sure the quality of the proposed documents using TAU and BLEU, using as reference the OSO. In Table 1, we report the performance of four search algorithms. The first three, IDL-CH-A , IDL-CH-HB , and IDL-CH-HB are the IDL- based search algorithms of Section 3, implement- ing A search, histogram beam search with a beam of 100, and histogram beam search with a beam of 1, respectively. We compare our algo- rithms against the greedy algorithm used by La- pata (2003). We note here that the comparison is rendered meaningful by the observation that this algorithm performs search identically with al- gorithm IDL-CH-HB (histogram beam 1), when setting the heuristic function for future costs to constant 0. The results in Table 1 clearly show the superi- ority of the IDL-CH-A and IDL-CH-HB algo- 808 rithms. Across all models considered, they consis- tently propose documents with scores at least as good as OSO (0% Estimated Search Error). As the original documents were coherent, it follows that the proposed document realizations also ex- hibit coherence. In contrast, the greedy algorithm of Lapata (2003) makes grave search errors. As the comparison between IDL-CH-HB and IDL- CH-HB shows, the superiority of the IDL-CH al- gorithms depends more on the admissible heuristic function than in the ability to maintain multiple hypotheses while searching. 4.3 Evaluation of Log-linear Models For this round of experiments, we held con- stant the search procedure (IDL-CH-HB ), and varied the parameters of Equation 1. The utility-trained log-linear models are compared here against a baseline log-linear model log- linear , for which all parameters are set to 1, and also against the individual models. The results are presented in Table 2. If not properly weighted, the log-linear com- bination may yield poorer results than those of individual models (average TAU of .34 for log- linear , versus .38 for IBM and .39 for CM, on the EARTHQUAKES domain). The highest TAU accuracy is obtained when using TAU to per- form utility-based training of the parameters (.47 for EARTHQUAKES, .50 for ACCIDENTS). The highest BLEU accuracy is obtained when us- ing BLEU to perform utility-based training of the parameters (.16 for EARTHQUAKES, .24 for the ACCIDENTS).For both genres, the differences between the highest accuracy figures (in bold) and the accuracy of the individual models are statis- tically significant at 95% confidence (using boot- strap resampling). 4.4 Overall Performance Evaluation The last comparison we provide is between the performance provided by our framework and previously-reported performance results (Table 3). We are able to provide this comparison based on the TAU figures reported in (Barzilay and Lee, 2004). The training and test data for both genres is the same, and therefore the figures can be di- rectly compared. These figures account for com- bined model and search performance. We first note that, unfortunately, we failed to accurately reproduce the model of Barzilay and Lee (2004). Our reproduction has an average TAU figure of only .39 versus the original fig- ure of .81 for EARTHQUAKES, and .36 versus .44 for ACCIDENTS. On the other hand, we repro- duced successfully the model of Barzilay and La- pata (2005), and the average TAU figure is .19 for EARTHQUAKES, and .12 for ACCIDENTS 3 . The large difference on the EARTHQUAKES corpus be- tween the performance of Barzilay and Lee (2004) and our reproduction of their model is responsi- ble for the overall lower performance (0.47) of our log-linear model and IDL-CH-HB search algorithm, which is nevertheless higher than that of its component model CM (0.39). On the other hand, we achieve the highest accuracy figure (0.50) on the ACCIDENTS corpus, out- performing the previous-highest figure (0.44) of Barzilay and Lee (2004). These result empirically show that utility-trained log-linear models of dis- course coherence outperform each of the individ- ual coherence models considered. 5 Discussion and Conclusions We presented a generic framework that is capa- ble of integrating various stochastic models of dis- course coherence into a more powerful model that combines the strengths of the individual models. An important ingredient of this framework are the search algorithms based on IDL-expressions, which provide a flexible way of solving discourse generation problems using stochastic models. Our generation algorithms are fundamentally differ- ent from previously-proposed algorithms for dis- course generation. The genetic algorithms of Mellish et al. (1998) and Karamanis and Man- arung (2002), as well as the greedy algorithm of Lapata (2003), provide no theoretical guarantees on the optimality of the solutions they propose. At the other end of the spectrum, the exhaus- tive search of Barzilay and Lee (2004), while en- suring optimal solutions, is prohibitively expen- sive, and cannot be used to perform utility-based training. The linear programming algorithm of Althaus et al. (2005) is the only proposal that achieves both good speed and accuracy. Their al- gorithm, however, cannot handle models with hid- den states, cannot compute -best lists, and does not have the representation flexibility provided by 3 Note that these figures cannot be compared directly with the figures reported in (Barzilay and Lapata, 2005), as they use a different type of evaluation. Our EB model achieves the same performance as the original Syntax+Salience model, in their evaluation setting. 809 IDL-expressions, which is crucial for coherence decoding in realistic applications such as multi- document summarization. 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